1) To select shapes you may use the cursor function mode select, this allows you to select all the shapes you want

programmatically you will have a button in a tool strip and pressing this button you should execute the following code:

Map1.FunctionMode = FunctionMode.Select

to get the selected features programmatically you may access to

yourlayer.Selection

to cycle through all the features you selected I think the code is like

foreach feature as Ifeature in yourlayer.Selection
'your code
next

the selection can be converted to a featureset or to a featurelist through yourlayer.Selection.ToFeatureSet and yourlayer.Selection.ToFeaturelist.
If you want to display attributes of the selected features to a datagridview (I called it DGVAttributeTable) you can write the following code